A219367 Number of n X 2 arrays of the minimum value of corresponding elements and their horizontal or vertical neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..3 n X 2 array.

4, 13, 60, 193, 514, 1231, 2748, 5802, 11665, 22432, 41419, 73698, 126799, 211612, 343525, 543837, 841488, 1275151, 1895734, 2769343, 3980760, 5637493, 7874458, 10859356, 14798811, 19945338, 26605213, 35147320, 46013053, 59727354, 76910971

Offset

1,1

Comments

Column 2 of A219373.

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = (1/13440)*n^8 + (1/3360)*n^7 + (1/576)*n^6 + (41/240)*n^5 - (9419/5760)*n^4 + (2009/160)*n^3 - (70291/2016)*n^2 + (42649/840)*n - 29 for n>1.

Conjectures from Colin Barker, Mar 11 2018: (Start)

G.f.: x*(4 - 23*x + 87*x^2 - 215*x^3 + 349*x^4 - 353*x^5 + 219*x^6 - 84*x^7 + 25*x^8 - 6*x^9) / (1 - x)^9.

a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>9.

(End)

Example

Some solutions for n=3:
..0..0....0..0....1..1....2..2....0..0....0..0....2..1....1..0....2..0....2..0
..0..1....0..1....1..1....2..2....0..0....0..2....1..1....0..0....0..0....0..0
..2..3....3..1....2..3....2..3....0..1....2..2....1..1....2..0....2..0....3..0

Crossrefs

Cf. A219373.

Sequence in context: A317891 A115455 A241470 * A149487 A372125 A320359

Adjacent sequences: A219364 A219365 A219366 * A219368 A219369 A219370

Keyword

nonn

Author

R. H. Hardin, Nov 19 2012

Status

approved